Implementing the RFT finite-volume formalism for three pions across all non-maximal isospins

Abstract

We present a numerical investigation of the relativistic-field-theoretic (RFT) formalism, used to predict the discrete energy spectrum of three pions in a finite volume. Applying the previously derived generalization, we extract results for all non-maximal isospin values ($I_{\pi \pi \pi }=2,1,$ and $0$), for different total momenta $\mathbf{P}$, and for various irreducible representations of the finite-volume symmetry group. We restrict attention to the unphysical scenario in which the three-particle interactions are set to zero. This set-up thus serves as a baseline for future lattice QCD calculations that will aim to extract such three-body interactions.

Comments: 12 pages, 4 figures, Contribution to Lattice 2024